Weak solutions to a Penrose-Fife model with Fourier law for the temperature
The author considers an initial-boundary value problem for the system \[ \tau \varphi_t - \xi^2 \Delta\varphi + a (\varphi^3 - \varphi) = b/\theta, \qquad c\theta_t - K \Delta \theta = b \varphi_t \] in \(N\leq 3\) space dimensions, where \(a,b,c,\theta,\xi,K\) are constants. Under the assumption that the initial temperature is positive almost everywhere, he proves the existence of a global weak solution with \(\theta > 0\) almost everywhere.
scientific article; zbMATH DE number 1215739